Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22554079 | C2 | semidirect |
| 2. #22553434 | C2 | semidirect |
| 3. #22553429 | C2 | semidirect |
| 4. #22553361 | C2 | semidirect |
| 5. C2×#16862173 | C2 | semidirect |
| 6. M16×Dic131 | C2 | semidirect |
| 9. #16862253 | C22 | semidirect |
| 14. #16862182 | C22 | semidirect |
| 15. #16862173 | C22 | semidirect |
| 16. #16862173 | C22 | semidirect |
| 17. #16862156 | C22 | semidirect |
| 18. C8×Dic131 | C22 | semidirect |
| 20. #137×C131 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C131 | C4 | semidirect |
| 44. Q16×C131 | C2×C4 | semidirect |
| 45. SD16×C131 | C2×C4 | semidirect |
| 46. D8×C131 | C2×C4 | semidirect |
| 85. C131 | #2956 | semidirect |
| 95. #137 | Dic131 | semidirect |
| 96. AGL(1,ℤ/8) | Dic131 | semidirect |
| 120. Q16 | C2×Dic131 | semidirect |
| 121. SD16 | C2×Dic131 | semidirect |
| 122. D8 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554079 | 2 |
| #22553434 | 2 |
| #22553429 | 2 |
| #22553361 | 2 |
| C2×#16862173 | 2 |
| M16×Dic131 | 2 |
| #575×C131 | 2 |
| #2956 | 131 |